# Discriminant functions for formative conditions of bedforms in open-channel flows

## Discriminant functions for formative conditions of bedforms in open-channel flows

This study provides boundary surfaces of bedform phases defined as discriminant functions of dimensionless parameters. The following is the method for caluculating the functions.

First of all, we defined new bedform phase diagrams using three parameters in dimensionless form.

On the basis of the diagram described above, discriminant functions are derived. The discriminant functions of bedforms obtained in this study can serve quantitative paleo-flow analysis of sedimentary structures. Their form is ƒ(D*, τ*, Fr) = 0 or ƒ(D

_{0}, U_{0}, h_{0}) . This function can be recast in the form U = ƒ(D, h), where U = flow velocity; D = sediment particle size; h = flow depth. Thus, when we obtain the data of sediment particle size and flow depth from sedimentary structures, we can estimate paleo-flow velocity. The discriminant functions are useful and objective for estimation of paleo-flow conditions.This work is published on Journal of Geophysical Research: Earth Surface, and the data source can be downloaded (http://onlinelibrary.wiley.com/doi/10.1002/2017JF004290/full).

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